The chirp modulation method is a modulation method in which the frequency of a signal (chirp) varies linearly over time in a bandwidth of Fs Hz. A chirp having a positive gradient in the frequency-time plane is generally referred to as an up-chirp, for example chirp 1 and chirp 2 on FIG. 1. A chirp having a negative gradient in the frequency-time plane is generally referred to as a down-chirp, for example chirp 3 on FIG. 1.
A chirp can be represented by a sequence of N samples. One or more identical contiguous chirps can form a symbol that represents a data value to be communicated. A chirp can be represented mathematically as:C(g,p)=ejπg(n−fn(p)(n+1−fn(p))/N  (equation 1)where g is the gradient of the chirp, N is the number of samples in the sequence, n is a sample in the sequence, p is the symbol's value, fn(p) is a function that encodes p onto the received chirp, which implicitly may also be a function of g, n, N and other constants, and C is the received chirp sequence, which is normally evaluated for all integer values of n from 0 to N−1 in order. The number of valid values of p is the symbol set size, which is nominally N. However, the symbol set size can be more or less than N depending on the quality of the link. The value of g can have any value greater than 0 and less than N. Preferably, g is an integer between 1 and N−1. Due to the modular nature of this expression negative gradients are obtained from N−1 backwards. Hence, N−2 is equivalent to a negative gradient of −2. Where there are more than one identical contiguous chirps in a symbol, each chirp individually conveys the same value which is the symbol value of the symbol.
Chirp 1 in FIG. 1 has a starting frequency of −Fs/2 and a gradient of 1. It increases linearly in frequency over a period of N samples at a sample rate of Fs to reach a frequency close to +Fs/2. Since this is a complex sampled system +Fs/2 is the same as −Fs/2. Multiple chirps are usually contiguous but may start with a different frequency. The signal phase is typically made continuous throughout a sequence of chirps. In other words, after the signal has reached +Fs/2 at n=N−1, the next symbol starts with n=0 again. FIG. 1 illustrates an example in which two consecutive chirps have the same symbol value, whereas the third chirp is different. An apparent discontinuity in frequency between chirp 1 and chirp 2 occurs at n=N.
Chirp 4 in FIG. 2 has a gradient of 2 and a starting frequency of −Fs/2. Because it has double the gradient of the chirps of FIG. 1, it increases linearly in frequency to +Fs/2 in half the number of samples that the chirps in FIG. 1 do, i.e. it reaches close to +Fs/2 after close to N/2 samples. The chirp then wraps around in frequency. Since this is a sampled system, these frequency wraps are in effect continuous and have continuous phase. The chirp repeats the frequency sweep from −Fs/2 to +Fs/2 between samples N/2 and N.
The chirps also have continuous frequency and phase from one end of the chirp to the other. A cyclic shift of the samples that make up a chirp creates another valid chirp.
In communications systems in which a transmitting device desires to communicate with a specific remote device, the transmitting device “addresses” the remote device in order to establish a connection with that remote device. It is known to address a specific device by using a specific frequency associated with that device. This approach is problematic because the number of receivers that the transmitting device can address is limited by the number of distinct frequencies available. More advanced schemes involve a transmitter broadcasting an “address” packet identifying a specific device it wants to connect to. A plurality of devices receive the address packet and decode it in order to determine if the following transmission is intended for them. The identified device then continues to receive the remaining transmission from the transmitter. In a modification of this approach, it is known to include the receiver's address in the header of a packet, the payload of which includes the message to be communicated to that specific device. In both of these two latter approaches, part or whole packets which could otherwise have been used to carry traffic data, are used solely to carry addressing information.
Using whole or part packets for addressing is suitable for systems utilising high data rates, and operating on devices having large energy reserves. However, chirp communications are typically used in systems operating using low data rates and short messages and in environments where there could be multiple simultaneous transmitting devices. When operating using low data rate chirp signals, using part or whole chirp signals to carry the address of the receiver further significantly reduces the amount of traffic data that can be carried by the chirp signals. Additionally, chirps signals are typically communicated between low power devices, for example battery powered handheld devices. The processing power required to decode the addressing chirps in addition to the chirps carrying traffic data is an additional source of power drain for a low power device. Furthermore, low power receivers are typically only able to listen to a single transmitter at a time. When there are many transmitting devices, particularly when they are using the same frequency, a receiver may find itself receiving and decoding the addresses of many messages, most of which will be unwanted. Not only is this an additional power drain, the receiver may miss a wanted message because it happened to be receiving and decoding an unwanted message at that time.
Thus, there is a need for an improved method of addressing chirp communications to a particular receiver which is suitable for systems operating using low data rates, low power and short messages and in environments where there could be multiple simultaneous transmitting devices.